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A081253 Numbers k such that A081252(m)/m^2 has a local minimum for m = k.

%I A081253 #34 May 23 2022 07:54:54
%S A081253 2,4,9,18,37,74,149,298,597,1194,2389,4778,9557,19114,38229,76458,
%T A081253 152917,305834,611669,1223338,2446677,4893354,9786709,19573418,
%U A081253 39146837,78293674,156587349,313174698,626349397,1252698794,2505397589
%N A081253 Numbers k such that A081252(m)/m^2 has a local minimum for m = k.
%C A081253 The limit of the local minima, lim_{n->infinity} A081252(n)/n^2 = 1/14. For local maxima cf. A081254.
%H A081253 Michael De Vlieger, <a href="/A081253/b081253.txt">Table of n, a(n) for n = 1..3321</a>
%H A081253 Klaus Brockhaus, <a href="/A053646/a053646.gif">Illustration for A053646, A081252, A081253 and A081254</a>
%H A081253 Chris J. Mitchell and Peter R. Wild, <a href="https://arxiv.org/abs/2108.03069">Constructing orientable sequences</a>, arXiv:2108.03069 [math.CO], 2021. See Table 2 p. 12 but with different offset.
%H A081253 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-2).
%F A081253 a(n) = floor(2^(n-1)*7/3).
%F A081253 a(n) = a(n-2) + 7*2^(n-3) for n > 2; a(n+2) - a(n) = A005009(n-1); a(n+1) - a(n) = A062092(n-1).
%F A081253 G.f.: -x*(x^2 - 2)/((x - 1)*(x + 1)*(2*x - 1)).
%F A081253 a(n) = 2*a(n-1) for even n, otherwise a(n) = 2*a(n-1)+1, with a(1)=2. - _Bruno Berselli_, Jun 19 2014
%e A081253 9 is a term since A081252(8)/8^2 = 5/64 = 0.078, A081252(9)/9^2 = 6/81 = 0.074, A081252(10)/10^2 = 8/100 = 0.080.
%t A081253 Rest@ CoefficientList[Series[-x (x^2 - 2)/((x - 1) (x + 1) (2 x - 1)), {x, 0, 31}], x]
%o A081253 (Python) print([7*2**n//6 for n in range(1, 50)]) # _Karl V. Keller, Jr._, May 22 2022
%Y A081253 Cf. A053646, A081252, A081254, A005009, A062092.
%Y A081253 Cf. A266071 (binary).
%K A081253 nonn,easy
%O A081253 1,1
%A A081253 _Klaus Brockhaus_, Mar 17 2003
%E A081253 Formulas adjusted to be consistent with offset 1 by _Pontus von Brömssen_, Sep 27 2021